Structure and Bonding of Alkali-Metal Pentalenides - Organometallics

Article pubs.acs.org/Organometallics

Structure and Bonding of Alkali-Metal Pentalenides Jorge Barroso,† Sukanta Mondal,† José Luis Cabellos,† Edison Osorio,‡ Sudip Pan,*,† and Gabriel Merino*,† †

Departamento de Física Aplicada, Centro de Investigación y de Estudios, Avanzados Unidad Mérida, km 6 Antigua carretera a Progreso, Apdo. Postal 73, Cordemex, 97310 Mérida, Yucatán, México ‡ Departamento de Ciencias Básicas, Universidad Católica Luis Amigó, SISCO, Transversal 51A #67B 90, Medellín, Colombia S Supporting Information *

ABSTRACT: The lowest energy isomers of alkali-metal pentalenides, E2C8H6 (E = Li, Na, K, Rb, Cs), are inverted sandwiches. Along Li to Cs, the location of the E atoms shifts toward the points over the center of the pentalene moiety even in the presence of solvent molecules such as dimethoxyethane. Adaptive natural density partitioning analysis reveals the equivalent 10 πbonding frameworks in the C8H62− and E2C8H6 systems. The stability of these complexes practically originates from the electrostatic interaction (84−92%) between C8H62− and [E···E]2+. While the sharp drop in interaction energy in Na complex, in comparison to that in the Li analogue, is due to the lower contribution from both electrostatic (by 31.6 kcal mol−1) and orbitalic (by 48.1 kcal mol−1) terms, for the rest of the complexes the obtained trend of interaction energy originates from the reduced ionic contacts. Although the orbital interaction is less important in these complexes, it plays an important role in deciding their geometries. The obtained geometrical change along Li to Cs is a consequence of the participation of the d orbitals in the heavier analogues.

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INTRODUCTION In 1922, Armit and Robinson suggested pentalene to be an aromatic hydrocarbon, but in constrast to benzene, this molecule tends to form its dimer.1 This instability was rationalized later on via Hückel’s rule, which predicts that while pentalene with 8 π-electrons should be classified as antiaromatic, the corresponding dianion, a 10-π-electron system, should be aromatic.2 Therefore, the instability of these two fused five-membered rings is basically attributed to its antiaromatic character. In 1962, Katz and Rosenberger synthesized dilithium pentalenide (Li2C8H6).3 This complex is formed by the double deprotonation of dihydropentalene with n-BuLi in THF solution. Almost 20 years later, Stezowski et al. reported the crystal structure of the dilithium pentalenide dimethoxyethane complex, which has both lithium atoms capping different rings on opposite faces.4 Cloke et al. synthesized the crystal of a dipotassium pentalenide derivative, [C8H4(SiiPr3-1,4)2]K2, by treating the trialkylsilyl-substituted dihydropentalene with KNH2 in diethyl ether.5 Interestingly, no other alkali-metal pentalenide has been synthesized so far. This is because of the practical difficulties in the synthesis of precursors for the pentalene dianion.6 Nevertheless, pentalene derivatives have been used to synthesize full, half, and mixed sandwich compounds of transition metals, lanthanides, and actinides.7 As a ligand, pentalene has the ability to act as a cyclopentadienyl or allyl anion, as a folded η8-bonding ligand, or as a bridging ligand in bimetallic systems. For more details about the reported work on organometallic chemistry of pentalene and pentalene derivatives, the reader is referred to the excellent review by Summerscales and Cloke.8 © XXXX American Chemical Society

Given the very sparse information about the heavier congeners of dilithium pentalenide, herein we report the structure and bonding of the dialkalipentalenide complexes E2C8H6 (E = group 1 metals) via density functional theory (DFT) computations. We found that while the lowest energy forms of the Na and K complexes have C2h symmetry, such as that reported for the Li congener,3 the Rb and Cs complexes adopt perfect D2h structures, in such a way that the metal atoms interact with all eight carbon atoms. Gagliardi and Pyykkö proposed that cesium and barium can be regarded as an “honorary” d element.9 Therefore, we can expect the participation of the Cs d orbitals in the formation of the title complexes. Further, the effect of complexation with two, four, and six dimethoxyethane (DME) molecules on the structures and stabilities of these alkali pentalenides is also studied. The nature of the metal−ligand bonding is examined using natural bond orbital (NBO)10−12 analysis and energy decomposition analysis (EDA) in conjunction with natural orbital for chemical valence (NOCV).13,14 Finally, to reveal the delocalized bonding in the studied pentalenides, the adaptive natural density partitioning (AdNDP) approach is used.15

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COMPUTATIONAL DETAILS

In order to explore the potential energy surfaces (PESs) of the E2C8H6 complexes, a modified Kick methodology was used as implemented in the Bilatu program.16−19 The search was restricted to those forms obtained from the interaction between a pentalenide fragment and two E atoms, considering only the singlet state. Thus, strictly speaking, we Received: October 4, 2016

A

DOI: 10.1021/acs.organomet.6b00768 Organometallics XXXX, XXX, XXX−XXX

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Organometallics

Figure 1. PBE0-D3/def2-TZVP structures of E2C8H6. Relative energies, including the ZPE correction, with respect to the lowest energy minimum are given in parentheses and the relative energies at the CCSD(T)/def2-TZVP//PBE0-D3/def2-TZVP level, including ZPE correction at the PBE0D3/def2-TZVP are given within brackets (in kcal mol−1). explored only a region of the PESs of such aggregates. The initial search was done at the PBE0/def2-SVP level.20,21 The structures obtained at this level were further reminimized and characterized using harmonic vibrational frequency analysis at the PBE0/def2-TZVP level, including dispersion via Grimme’s DFT-D3 approximation.22 For Rb and Cs atoms, quasi-relativistic pseudopotentials were used.23 We further rechecked the structures at the M06-2X/def2-TZVP level to verify that the present results are not an artifact of a particular level (see Tables S1 and S2 in the Supporting Information). The almost similar results at these two levels enabled us to proceed with the PBE0D3/def2-TZVP level. In the cases of Li and Na complexes, single-point energies were computed at the CCSD(T)/def2-TZVP//PBE0-D3/ def2-TZVP level. For the Li2C8H6·2DME complex, the corresponding geometry was taken from the crystal structure reported by Stezowski et al.,4 and the structures of its heavier analogues were modeled just by substituting two Li atoms with E atoms. For the larger DME complexes, free optimizations were done by arranging the DME molecules in a way that two oxygen centers of each DME molecule can interact with E

centers; at the same time there remains some space between two DME molecules to minimize the steric repulsion. For all of the DME complexes, the optimizations and vibrational frequency analyses were accomplished at the PBE/def2-TZVP level including the DFT-D2 dispersion correction.24 The reason for this is that, in the D3 expressions, one of the terms depends on the number of coordination of the involved atoms. When the coordination numbers turn out to be ∼8 or higher, the analytical expression for the second derivative of such term becomes unstable. In some cases, these complexes have centers possessing ∼8 or higher coordination number. All of these computations were done using the Gaussian 09, Revision D.01, program package.25 Atomic charges (q) and Wiberg bond indices (WBIs) were computed by using the NBO partitioning scheme.10−12 The nature of the chemical bond was also analyzed by EDA-NOCV at the PBED3/TZ2P//PBE0-D3/def2-TZVP level using the ADF (2013.01) package.26 Instead of the frozen core approximation, an all-electron basis set was used. Scalar relativistic effects in the heavy elements were considered using the zeroth-order regular approximation.27−29 B


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Organometallics

kcal mol−1). The reason is related to their large atomic sizes, due to which either two isomers get converged into a single isomer or the similar isomers corresponding to their lighter analogues become unstable owing to repulsion between two positively charged E centers. A summary of the lowest lying structures for the alkali-metal pentalene complexes is depicted in Figure 2 with the important structural parameters. With an

In EDA calculations, the interaction energy (ΔEint) between two fragments is decomposed into four energy terms: viz., the electrostatic interaction energy (ΔVelstat), the Pauli repulsion (ΔEPauli), the orbital interaction energy (ΔEorb), and the dispersion interaction energy (ΔEdisp). Therefore, ΔEint between two fragments can be written as

ΔE int = ΔVelstat + ΔE Pauli + ΔEorb + ΔEdisp

(1)

The reader is referred to two excellent reviews on EDA for more details.13,14 So far, we have successfully reported studies on metallocene, half sandwich, and inverted sandwich type structures using EDA.30−38 The nature of chemical bonding was also analyzed using the AdNDP method developed by Zubarev and Boldyrev.15 This technique constitutes the concept of electron pairs as the fundamental component of chemical bonding. It describes the electronic structure of molecules in terms of n-center−two-electron (nc-2e) bonds, where n = 1 up to the total number of atoms in the studied system. AdNDP retrieves both Lewis bonding concepts (lone pairs or 2c-2e bonds) and delocalized bonding elements.

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Figure 2. PBE0-D3/def2-TZVP lowest-lying energy structures of E2C8H6 (E = Li, Na, K, Rb, Cs). The distances of the E atoms from the ring centers and the C−C bond lengths (in Å) are shown.

STRUCTURES AND ENERGETICS The lowest energy isomer of Li2C8H6, obtained via our unbiased potential energy surface exploration, forecasts the singlet C2h inverted sandwich, in which both lithium atoms are involved in η5 bonding on opposite faces at different rings (Figure 1). At 8.5 kcal mol−1 with respect to the lowest lying isomer, another C2v inverted sandwich type form is noted, but the Li atoms are bonded to the same ring at opposite faces. One feature in the next two lowest energy isomers is that both Li atoms are present at the same side of the pentalene. The repulsion between two Li+ centers residing at the same side of the pentalene moiety makes these isomers higher energy structures (more than 12 kcal mol−1).39 Let us define the angle θ (Figure 1) as joining C2, the center of the pentalene (the midpoint of bridging carbons C7 and C8), and the metal atom above the pentalene in the lowest lying isomers of E2C8H6 for further discussion and comparison. The lowest energy geometry of Na2C8H6 is similar to that of Li2C8H6, though a clear change in θ (59.8° for Li and 68.3° for Na) is perceived. In contrast to the Li analogue, a structure the same as that of the second lowest energy isomer of Li2C8H6 is not found by our PES exploration for the Na congener; rather, the second and third lowest energy isomers at 20.5 and 26.9 kcal mol−1 are very similar to the third and fourth forms of Li2C8H6, respectively. Another form, having the C2 symmetry point group, is found at 28.1 kcal mol−1, where also both Na atoms are present at the same side of the pentalene unit.40 The change in θ is even more pronounced in the K complex: i.e., along Li to K the metal atoms are gradually moving toward the point over the center of the planar pentalene. In the lowest energy isomer, 19.9° shift in θ is found along Li (θ = 59.8°) to K (θ = 79.7°) complex. For potassium, another couple of lower energy isomers are located at 30.1 and 32.8 kcal mol−1 bearing C2v and C1 symmetry, respectively. The C2v structure is likely to the second lowest lying form of Na, whereas the C1 like geometry is not found in the lighter congeners. Interestingly, for the lowest lying isomers of Rb2C8H6 and Cs2C8H6, the metal atoms are bonded with the pentalene core through η8 linkages, yielding a D2h point group in the resulting complexes. The next lowest energy isomers of Rb and Cs are noted at 33.4 and 37.0 kcal mol−1, respectively, with C1 symmetry, akin to the C1 isomer of the K congener. Note that the number of possible isomers is reduced to only two for Rb and Cs analogues within the selected energy window (40

increase in the size of the alkali metal, although their location becomes distant from the pentalene frame due to their increased radii, the extent of interaction changes, which is evident from the shortening of the C−C bonds (Figure 2) along Li to Cs pentalenides. The bond dissociation energies (BDEs) for the lowest lying isomers are computed considering the dissociation into neutral as well as charged species as E 2C8H6 → EC8H6 + E −

(2) +

E 2C8H6 → EC8H6 + E

(3)

E 2C8H6 → C8H6 + 2E E 2C8H6 → C8H6

2−

(4) +

+ 2E

(5)

Fragmentation to the neutral species following both schemes, dissociations of one metal from E2C8H6 (eq 2, ΔE1) and both the metals from E2C8H6 (eq 4, ΔE2), reveals the stability order Li2C8H6 > Cs2C8H6 > K2C8H6 > Rb2C8H6 > Na2C8H6, whereas in ionic dissociation (eqs 3 and 5, ΔE3 and ΔE4, respectively), a gradual decreasing stability trend is found in both dissociation paths on moving down the alkali-metal group (see Table 1). The BDEs for the Li complex are substantially higher in all cases, ΔE1 = 59.6 kcal mol−1, ΔE2 = 171.4 kcal mol−1, ΔE3 = 122.4 kcal mol−1, and ΔE4 = 441.7 kcal mol−1, in comparison to those for the heavier congeners. The natural charge on each E Table 1. Dissociation Energies of the Complexes Computed at the PBE0-D3/def2-TZVP Levela system

ΔE1

ΔE2

ΔE3

ΔE4

Li2C8H6 Na2C8H6 K2C8H6 Rb2C8H6 Cs2C8H6

59.6 35.7 39.9 37.9 46.2

171.4 146.4 131.7 128.2 125.7

122.4 78.5 90.7 87.1 102.0

441.7 (438.7) 384.5 (378.9) 354.7 343.5 344.4

Energy values are given in kcal mol−1. The values include the ZPE correction. The values in parentheses are at the CCSD(T)/def2TZVP//PBE0-D3/def2-TZVP level.

a

C


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Organometallics

Figure 3. PBE-D2/def2-TZVP minimum energy structures of E2C8H6·nDME (E = Li, Cs; n = 2, 4, 6). The distances (in Å) of the E atoms are from the center of the ring for Li and from the center of pentalene for Cs.

center and the aromatic behavior of the C8H62− moiety suggest that ionic dissociation is more likely to occur than the neutral dissociation (vide infra).

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Although the overall movement of E atoms toward the point over the center of the pentalene moiety along Li to Cs persists in the presence of DME molecules, the degree of such transfer diminishes to some extent. This is more prominent in the case of Rb2C8H6, where in the presence of both 2DME and 4DME one Rb atom does not reside perfectly over the center of C8H6, in contrast to the case for the bare structure (see Figure S1 in the Supporting Information). The alkali metals are closer to the pentalene moiety by 0.190 (Li), 0.115 (Na), 0.088 (K), 0.098 (Rb), and 0.055 Å (Cs) in comparison to the two DME coordinated complexes (Figures 2 and 3 and Figure S1). Moreover, such data become even larger, 0.267 (Li), 0.174 (Na), 0.169 (K), 0.125 (Rb), and 0.059 Å (Cs), in comparison to the complexes of 4DME. Thus, as the number of coordinated DME molecules increases, the distance between E atoms and the pentalene fragment increases, which in turn hints at the decreased interaction between E atoms and the pentalene in the presence of DME molecules. Complexation energies (ΔEcomplex) for the successive coordination of E2C8H6 with DME molecules are computed (Table 2). The ΔEcomplex values for the formation of E2C8H6· 2DME lie within the range of −32.1 to −56.5 kcal mol−1 for Li−Rb analogues, being the largest for the Li case, and thereafter these values gradually decrease on moving from Li to Rb. In the case of Cs (−35.6 kcal mol−1), a slight increase in ΔEcomplex is noted. On the other hand, the ΔEcomplex values for

COMPLEXATION EFFECTS

What is the effect of complexation with DME molecules on the structure and stability of the lowest-lying Li−Cs pentalenides? Previously Schleyer and co-workers investigated the structure of Li2C8H6·2DME both experimentally and theoretically.4 Along the same lines, we have studied the consequences of the proximity of DME molecules on the alkali-metal pentalenides. In Li2C8H6·2DME (Figure 3), while the calculated average distance of the Li atoms from the coordinating oxygen atoms is 2.07 Å, the Li atoms are located nearer to C1−C3 (average distance 2.23 Å) than to the bridgehead carbons (C7, C8) (average distance 2.28 Å). Importantly, the corresponding distances match excellently with the experimental values (2.01, 2.22, and 2.31 Å, respectively) reported by Schleyer and coworkers.4 Similarly to the crystal structure, in the optimized geometry of Li2C8H6·2DME, the DME molecules interact with Li atoms through their oxygen centers located almost perpendicular to the pentalene ring. However, on going from Li to its heavier analogues, a significant change in the orientation of DME is noted where one DME reorients itself in a tilted way. Nevertheless, the basic structural pattern in the E2C8H6 moiety remains more or less unchanged. D


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Organometallics Table 2. Complexation Energies (ΔEcomplex) and Complexation Free Energy Changes (ΔGcomplex), Computed at the PBE/def2-TZVP Level Including DFT-D2 Dispersion Correction, using the Schemes (1) E2C8H6 + 2DME → E2C8H6·2DME, (2) E2C8H6·2DME + 2DME → E2C8H6· 4DME, and (3) E2C8H6·4DME + 2DME → E2C8H6·6DMEa ΔEcomplex (kcal mol−1)

a

Table 3. Wiberg Bond Indices of C−C (WBIC−C) and C−E (WBIC−E) Bonds, NPA Charges at the E Center (q(E), |e|), and the Lowest Harmonic Vibrational Frequencies (νmin, cm−1) Computed at the PBE0-D3/def2-TZVP Level C8H62− Li2C8H6 Na2C8H6 K2C8H6 Rb2C8H6 Cs2C8H6

ΔGcomplex (kcal mol−1)

E

scheme 1

scheme 2

scheme 3

scheme 1

scheme 2

scheme 3

Li Na K Rb Cs

−56.5 −53.8 −35.9 −32.1 −35.6

−21.3 −30.1 −34.6 −32.4 −40.1

a a −17.8 −18.9 −42.5

−33.7 −29.5 −13.3 −10.6 −14.5

6.4 −4.2 −7.2 −7.3 −13.5

a a 7.0 8.1 −12.4

WBIC−C

WBIC−E

q(E)

νmin

1.32 1.32 1.32 1.32 1.32 1.32

0.01 0.01 0.01 0.01 0.01

0.94 0.97 0.96 0.96 0.93

149 183 64 7 23 37

AdNDP 15 analysis can depict the localized and/or delocalized bonding elements and, thereby, help in studying the delocalized character of a molecular motif. Though the pentalene dianion follows Hückel’s 4n + 2 rule for aromaticity,2 it is worth keeping in mind that the 4n + 2 rule was developed for monocyclic systems. However, later some advances were made by Platt41 as well as by Clar,42 who extended the limit to polycyclic systems as well. The delocalized bonding elements of C8H62− and E2C8H6 found by the AdNDP analysis are given in Figure 4. As one would expect, the AdNDP analysis localizes a classical σ-bonding framework in the C8H6 ring fragments composed of six 2c-2e C−H and nine 2c-2e C−C σ-bonds, with occupation numbers (ON) lying within the range 1.96− 2.00 |e|. The π-bonding skeleton for C8H62− involves five π molecular orbitals (MOs) delocalized on the two fused cyclopentadienyl carbon rings, with the ideal occupation number of 2.00 |e| implying its aromatic character. The πbonding frameworks for E2C8H6 complexes present exactly the same number of π orbitals as the C8H62− system, 10 π electrons delocalized over the C8H6 ring fragments. Of course, given that the system is fully delocalized, other possible bonding schemes could be found. Figure S2 in the Supporting Information shows an alternative scheme. Both are valid and provide the same number of π orbitals. Thus, the conclusion regarding aromaticity remains the same. Different energy components along with the interaction energies as obtained from EDA provide guidance in understanding the patterns of bonding in the title complexes. The choice of a proper partitioning scheme is very essential to get meaningful insight into the bonding. In general, when more than one partitioning scheme is possible, one should adopt that one which involves the smallest ΔEorb and ΔEPauli values.43 This is because of the fact that for these fragments the least alternation of the electronic charge distribution is required to form the electronic structure of the complex. Here, we have tested the neutral C8H6 and [E···E] as two interacting fragments; however, in all cases this scheme yields significantly higher ΔEorb and ΔEPauli values in comparison to those in the ionic partitioning scheme (Table 4 and Table S3 in the Supporting Information). Therefore, the latter scheme is more appropriate for an inspection of the bonding in the present cases. Of course, the corresponding natural charges on each fragments support this. Since Grimme’s dispersion correction is not available for PBE0 in ADF, we have tested the dispersion (ΔEdisp) contribution at the PBE-D3/TZ2P level (Table 4). Both the computed ΔEint values at the PBE0-D3/def2-TZVP level and the dissociation energies (ΔE4) show exactly the same trend as those of the ΔEint values at the PBE-D3/TZ2P level (Table 4).

Not computed.

the formation of the E2C8H6·4DME complexes from E2C8H6· 2DME are almost the same for K (−34.6 kcal mol−1), Rb (−32.4 kcal mol−1), and Cs (−40.1 kcal mol−1) in comparison to the corresponding values for E2C8H6·2DME from E2C8H6. In contrast, for the lighter congeners (Li, Na) such energy decreases considerably by 35.2 (Li) and 23.7 kcal mol−1 (Na) in the formation of 4DME analogues, which is due to the repulsion between the DME molecules coordinating at the same E (smaller size of Li and Na causing congested disposition of DMEs). To include the entropic factor for such aggregation, complexation free energy changes (ΔGcomplex) at 298 K are also evaluated (see Table 2). It is noted that, despite the attractive ΔEcomplex value of −21.3 kcal mol−1, the formation of Li2C8H6·4DME is not feasible, as indicated by the positive ΔGcomplex value, supporting the experimental evidence of the 2DME coordinated Li2C8H6 complex reported by Schleyer and co-workers.4 However, for its heavier homologues, E2C8H6 would coordinate with four DME molecules since the process E2C8H6·2DME + 2DME→ E2C8H6·4DME turns out to be exergonic in nature. We have further checked the possibility of 6DME coordinated complexes for K−Cs analogues, but due to the steric repulsion between DME molecules only the Cs2C8H6·6DME complex is found to be viable (see Figure S1 in the Supporting Information for minimum energy structures of K2C8H6·6DME and Rb2C8H6·6DME). Note that, despite the strong coordination of DME molecules with E, this does not alter the overall structural pattern in E2 C8 H6 moiety significantly.

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BONDING ANALYSIS In order to understand the pattern of bonding and the geometrical trend along the group, we have performed a set of computations including NBO,10−12 AdNDP,15 and EDA.13,14 The partial charges on alkali-metal atoms (0.93−0.97 |e|, Table 3) in E2C8H6 indicate a transfer of almost one electron from each alkali metal to the pentalene moiety in each complex, which in turn shows that the E atoms are interacting with the pentalene moiety electrostatically. The negligible WBI values of the C−E contacts support the inferred dominant ionic interaction therein. Therefore, clearly the carbon skeleton accepts a couple of electrons. Actually, average values of the WBIs of the C−C bonds in C8H62− and E2C8H6 remain unaltered (1.32), implying a similar bonding situation in both pentalenide cores. E


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Figure 4. Five multiple-center−two-electron π-bonding frameworks recovered by the AdNDP analysis for C8H62− and E2C8H6.

Table 4. Results of EDA Considering C8H62− and [E···E]2+ as the Interacting Fragments at the PBE-D3/TZ2P Levela pentalenide

ΔEint¶

ΔEint

ΔEPauli

ΔEdisp

Li2C8H6 Na2C8H6 K2C8H6 Rb2C8H6 Cs2C8H6

−532.5 −471.8 −443.2 −431.2 −431.5

−527.5 −453.8 −419.0 −408.2 −409.0

49.7 44.3 55.9 54.9 75.4

1.7 1.0 2.1 1.1 −0.8

ΔVelstat −490.5 −458.9 −431.0 −417.1 −418.3

(84.7) (91.9) (90.4) (89.9) (86.5)

ΔEorb −88.4 −40.3 −46.0 −47.1 −65.3

(15.3) (8.1) (9.6) (10.1) (13.5)

ag(σ) −20.1 −10.4 −10.4 −10.9 −14.9

(22.7) (25.8) (22.7) (23.6) (22.8)

bg(π⊥) −18.4 −8.4 −10.2 −10.3 −13.8

(20.8) (20.8) (22.2) (22.3) (21.1)

au(δ) −18.8 −7.5 −8.3 −8.0 −11.2

(21.3) (18.6) (18.1) (17.3) (17.2)

bu(π∥) −31.1 −14.0 −17.0 −17.9 −25.5

(35.2) (34.7) (37.0) (38.7) (39.1)

Energy values are given in kcal mol−1. The values in parentheses are the percentage contributions to the attractive interactions, ΔVelstat + ΔEorb. The values in parentheses are the percentage contributions to the total orbital interactions. ΔEint¶ indicates the interaction energy at the PBE0-D3/def2TZVP level. a

terms are almost the same, ΔEint is only marginally stronger in the former case than in the latter due to the larger Pauli repulsion (by 20.5 kcal mol−1) involved in Cs. Interestingly, dispersion interactions occurring between C8H62− and [E···E]2+ fragments are found to be repulsive in nature, except for Cs, which might seem to be counterintuitive. However, this is a consequence of the structure dependence of the C 6 coefficients in Grimme’s -D3 method. The C 6 coefficients in Grimme’s method depend on the coordination numbers of the atoms, which means that the C6 coefficients in the isolated [E···E]2+ species and in the complex are different. On the other hand, as in Grimme’s -D method, unlike the -D3 method, C6 does not depend on the atomic coordination, we have also performed EDA at the PBE-D/TZ2P level and found ΔEdisp terms as attractive in nature (Table S4 in the Supporting Information). Nevertheless, the contribution from ΔEdisp is least ca. 1−6% toward the total attraction. Since the orbital interactions may play an important role in deciding the geometry of the complexes, let us analyze the different irreducible representations raising the σ, π, and δ bonding partitions. It is found that more than 55% of the total orbital interaction originates from the in-plane and out-of-plane

In the present complexes, the preparation energies involved in the C8H6 fragments are quite low (≤0.5 kcal mol−1), implying very negligible distortion therein. However, to bring two E+ ions to those distances in the global minima, around 80.9−82.8 kcal mol−1 should be required. Nevertheless, the overall complexes are stable with respect to dissociation, as the repulsion between two E+ ions is overcompensated by the attractive interaction between C8H62− and two E+ ions. As expected from the ionic fragmentation, 84−92% of the total attraction between C8H62− and [E···E]2+ originates from ΔVelstat, whereas the orbital contact is responsible for only 8− 16% of the total attraction. The sharp drop in ΔEint (73.7 kcal mol−1) on going from Li to Na is due to the lower contribution from both ΔVelstat (by 31.6 kcal mol−1) and ΔEorb (by 48.1 kcal mol−1) in the Na complex in comparison to those in Li. Thereafter, there is no significant change in ΔEorb, except for Cs, in which an improved orbital contact is obtained. Therefore, for those cases gradually reduced ionic interaction between metals and C8H62− is responsible for the decreased stability on going down the group. Note that in the Cs complex, although the contribution from ΔEorb is significantly larger (by 18.2 kcal mol−1) than that in Rb but the corresponding ΔVelstat F


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Organometallics π interactions. Therefore, in terms of orbital participations they may be called π complexes. Further, with an increase in size of the alkali metal, the degree of π contributions also increases, except for Li. The plots of deformation density (Δρ) and the associated orbital interaction energies are provided in Figure 5.

larger if E resides above the C2 moiety, as a significant orbital contribution results from the electron shifting through C2 to E. Therefore, the obtained geometrical change along Li to Cs is a consequence of the participation of the d orbitals in the heavier analogues. In other words, although the interaction between C8H62− and [E···E]2+ is mostly electrostatic in nature, the orbital interaction has an important role in dictating the geometries of the studied complexes.

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SUMMARY The explorations of the potential energy surfaces of the alkalimetal pentalenide complexes (E2C8H6, E = Li, Na, K, Rb, Cs) show the lowest energy isomers being of inverted sandwich type, in which the alkali metals are located (approximately) above and below the different five-membered rings of C8H6 for E = Li, Na, K, whereas in Rb and Cs complexes the metal atoms reside at the points over the center of the pentalene moiety. The existence of five π bonds in the lowest energy isomers of C8H62− and E2C8H6 indicates the polycyclic aromatic situation in the C8H62− core. The computed bond dissociation energy (BDE) for the ionic dissociation channel of E2C8H6 producing C8H62− and two E+ reveals that the stability of the complexes along the dissociation gradually diminishes along Li to Rb, with a particularly sharp drop on moving from Li to Na. Cs2C8H6 has slightly improved stability in comparison to its Rb analogue. The attractive interaction between C8H62− and [E···E]2+ exclusively originates from the electrostatic contribution (ca. 84−92%). The sharp decrease in ΔEint (73.7 kcal mol−1) on moving from Li to Na is due to the lower contribution from both ΔVelstat (by 31.6 kcal mol−1) and ΔEorb (by 48.1 kcal mol−1) in the latter case in comparison to those in the former; after that, the reduced stability on going down the group is because of the reduced ionic interaction therein. The obtained change in geometry of E2C8H6 on moving from Li to Cs, particularly in the cases of Rb and Cs, is due to the involvement of d orbitals of E in the bonding. The effect of complexation with dimethoxyethane (DME) molecules on the structure and stability of E2C8H6 has been studied, which shows that the coordination of one, two, or three DME molecules to each E does not alter the structural pattern of the complexes significantly but it does increase the distances between E atoms and the pentalene core, in comparison to those in the bare complexes.

Figure 5. Plots of deformation densities, Δρ(r), of the pairwise orbital interactions of E2C8H6 (E = Li, Na, K, Rb, Cs) complexes at the PBED3/TZ2P//PBE0-D3/def2-TZVP level. The associated orbital interaction energies are given in kcal mol−1. The color code of the charge flow is red → blue. An isosurface value of 0.0005 au is used.

In the figure, the red region denotes Δρ(r) < 0 and the blue region denotes Δρ(r) > 0. In other words, the electron density shifts from the red to the blue region. As expected from the largest ΔEorb value in the case of Li, it involves a stronger pairwise orbital interaction in comparison to its heavier congeners. The largest contribution toward the total ΔEorb value originates from the shift of electron density around the C2 moiety to the vacant p orbitals of Li. Nevertheless, in the same pairwise orbital interaction the electron density is depleted from the C2 and C5 centers and it is shifted to Li through the adjacent carbon. Similarly, other Δρ(r) plots also show the electron density flow from the pentalene moiety to the Li atoms. The sharp drop in ΔEorb value on going from Li to Na is clearly understood from the corresponding Δρ(r) plots, where the orbital values associated with the C8H6→Na electron donation are significantly smaller than those in the Li case. In contrast, although the basic pattern of electron flow remains unaltered, the corresponding orbital values improve in K−Cs cases, due to the involvement of vacant d orbitals in the bonding. The participation of d orbitals is more prominent in Cs than in the others, supporting the argument of Gagliardi and Pyykkö to consider Cs as an “honorary” d element.9,38 Note that by symmetry the interaction with the d orbitals would be

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.organomet.6b00768. Results of EDA considering C8H6 and [E···E] as the interacting fragments at the PBE-D3/TZ2P level, results of EDA considering C8H62− and [E···E]2+ as the interacting fragments at the PBE-D/TZ2P level, structures of E2C8H6·nDME (E = Na−Rb) complexes, and results of AdNDP analysis (PDF) Cartesian coordinates of the studied complexes (XYZ)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail for S.P.: [email protected]. *E-mail for G.M.: [email protected]. G


Article

Organometallics ORCID

Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 09, revision D.01; Gaussian, Inc., Wallingford, CT, 2009. (26) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; FonsecaGuerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931−967. (27) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597−4610. (28) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1994, 101, 9783−9792. (29) van Lenthe, E.; Ehlers, A.; Baerends, E. J. J. Chem. Phys. 1999, 110, 8943−8953. (30) Merino, G.; Beltran, H. I.; Vela, A. Inorg. Chem. 2006, 45, 1091− 1095. (31) Velazquez, A.; Fernandez, I.; Frenking, G.; Merino, G. Organometallics 2007, 26, 4731−4736. (32) Cerpa, E.; Tenorio, F. J.; Contreras, M.; Villanueva, M.; Beltran, H. I.; Heine, T.; Donald, K.; Merino, G. Organometallics 2008, 27, 827−833. (33) Fernandez, I.; Cerpa, E.; Merino, G.; Frenking, G. Organometallics 2008, 27, 1106−1111. (34) Gomez-Sandoval, Z.; Peña, J.; Fonseca-Guerra, C.; Bickelhaupt, F. M.; Mendez-Rojas, A.; Merino, G. Inorg. Chem. 2009, 48, 2714− 2716. (35) Castro, A. C.; Johansson, M. P.; Merino, G.; Swart, M. Phys. Chem. Chem. Phys. 2012, 14, 14905−14910. (36) Castro, A. C.; Osorio, E.; Cabellos, J. L.; Cerpa, E.; Matito, E.; Solá, M.; Swart, M.; Merino, G. Chem. - Eur. J. 2014, 20, 4583−4590. (37) Vargas-Caamal, A.; Pan, S.; Ortiz-Chi, F.; Cabellos, J. L.; Boto, A.; Contreras-Garcia, J.; Restrepo, A.; Chattaraj, P. K.; Merino, G. Phys. Chem. Chem. Phys. 2016, 18, 550−556. (38) Mondal, S.; Cabellos, J. L.; Pan, S.; Osorio, E.; Torres-Vega, J. J.; Tiznado, W.; Restrepo, A.; Merino, G. Phys. Chem. Chem. Phys. 2016, 18, 11909−11918. (39) For example, to bring two Li+ ions to that distance in the isomer 3 of Li2C8H6, an energy of 119.7 kcal mol−1 should be required in contrast to the energy of 81.3 kcal mol−1 in the global minimum. On the other hand, isomer 3 also has a larger interaction energy by around 26.5 kcal mol−1 in comparison to that in the global minimum. The overall stability would depend on the balance between these two factors, given that the distortion within the pentalene moiety is almost negligible. Therefore, this clearly shows that the higher preparation energy involved within the Li2 fragment in the syn-corodinated isomer makes it a higher energy isomer in comparison to that of the anticoordinated global minimum energy isomer. (40) In both Li and Na cases the relative energies computed at the CCSD(T)/def2-TZVP//PBE0-D3/def2-TZVP level are very close to the values at the PBE0-D3/def2-TZVP level. (41) Platt, J. R. In Handbuch der Physik; Flugge, S., Ed.; SpringerVerlag: Berlin, 1961; pp 205−209. (42) Clar, E. The Aromatic Sextet; Wiley: London, 1972. (43) Tonner, R.; Frenking, G. Chem. - Eur. J. 2008, 14, 3260−3272.

Sukanta Mondal: 0000-0003-1918-8202 Edison Osorio: 0000-0001-7636-8168 Gabriel Merino: 0000-0003-1961-8321 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work in Mexico was supported by Conacyt (Grant CB́ 2015-252356 and Red Temática de Fisicoquimica Teórica). The CGSTIC (Xiuhcoalt) and ABACUS at Cinvestav (Conacyt grant EDOMEX-2011-COI-165873) are gratefully acknowledged for a generous allocation of computational resources. Contributions from Colombia were supported by Colciencias (Grant No. 211665842965). The authors thank Prof. Alvaro Muñoz-Castro for his helpful discussions.

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Structure and Bonding of Alkali-Metal Pentalenides - Organometallics

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